Centripetal Force Facts you must know if you are a PHYSICS student!

Centripetal force definition

Centripetal Force Definition– Centripetal force is a force which acts on a object rotating in a circular path. And this force acts in the direction towards the centre of the circle.This is the force which enables an object to continue its motion in a circular path.

Centripetal force facts and its concepts have always been in the favorites list of the students. Still we find many misconceptions and assumptions in their mind, around the fundamental concepts of this force.This post is on facts about Centripetal force. We have started with centripetal force definition and will finally cover an amazing example – Washing machine Centripetal force!

Centripetal force Example

We see many instances of the centripetal force being applied in the nature.

Applying the concepts of this force many devices like washing machine have been designed.

Students of fundamental physics should have a strong grasp on the concepts of this force. Here find a few important pointers with a detailed explanation of each which you will certainly like!

centripetal force

Horizontal circular motion and role of Gravity on the rotating object, irrespective of the centripetal force

Let’s tie a piece of stone to one end of a string and another end of the string is tied with a finger. Then start to rotate the stone with the help of the string in a horizontal plane. The stone starts moving in the horizontal circular track without any intention to drop towards the earth.

So how is this possible? How come it’s avoiding the effect of gravity?

Let’s find out. We all know that gravity works towards the center of the earth. As the stone is maintaining a circular path in a horizontal plane, its motion is at a right angle with the line of action of the gravity.

So do you think gravity has any effect on the stone piece rotating there?

centripetal force diagram1
Diagram-1

We can quickly check from the definition and formula of work done. Work done depends on the Cosine of the angle between the line of force and the displacement of the object.

But here what is the angle between the rotating stone and the line of gravity? Yes! It’s 90 degrees. And cos 90 degrees is zero.

What does this mean? This means work done on the rotating stone by the gravitational force of earth (gravity) is  ZERO. Therefore the gravity has no effect on its motion. Reference: Diagram-1

Centripetal Force & Newton’s First Law of Motion

How and Why Newton’s Law has come into this scenario? Continuing with what we were discussing, if the string is released suddenly, then what would happen?

The stone would fly off at a tangent to the circular path it was maintaining so far. It’s the demonstration of Newton’s First Law of Motion. How is that law being demonstrated here? Let’s discuss this.

As per the Law, an object with uniform velocity will continue to move in a straight line with the same velocity, if net force applied on it is zero.

But here we see as long as the string is intact, the tied stone can be given a circular motion. During this motion at every instance, its direction is changing. That means at every instance its velocity is changing! This again points to the fact that this motion is under acceleration!

So what can we derive from here? Yes, you are right!

There must be some force acting on the tied stone which is helping it to change its velocity at every moment. From the motion of the tied stone, it’s evident that the force is somehow working towards the center of the circular path.

And a special name is given to this force acting on a rotating object and directing towards the centre of the circular path. It’s called Centripetal Force. ( Reference: Fc shown in Diagram-1 )

centripetal force

Now how is this centripetal force being applied on the stone?

Of course, it’s being transferred from the finger to the stone and this transfer is happening via the string only.

Who is supplying this centripetal force here? The finger. That’s why when the string is released or the string is torn this force can’t pass to the stone anymore.

This is the instance when Newton’s First Law of motion comes into play. As there is no force (net force) on the stone so it will continue along its last direction on the circular path. And the direction is actually the tangent to that point on the circular path.

Centripetal Force – Who or What is supplying this?

1) In the above example, a stone is rotated in a horizontal plane with a string tied with a finger. Here the finger supplies the required centripetal force that makes the stone rotate. There are a few other instances when the supplier of this force varies from case to case.

2) Electron orbits the nucleus in an atom. The electrical attraction force generated between an electron and the nucleus supplies the centripetal force on the electron.

centripetal force-thorium-atom-circular motion


3) A car or a bike taking a circular bend – The Frictional force between the tires and the road supplies the required Centripetal force. (As it is a frictional force so certainly it has a maximum limit, beyond which balancing in a bike at a circular bend won’t be possible. It’s a different story, will take this in a separate post)

circular bend-friction

4) The satellite revolves around the earth. Here Gravitational Attraction between the earth and the satellite supplies this centripetal force.

centripetal force between earth and moon

To note that this centripetal force is a real force.

Centripetal Force formula

The formula of Centripetal force is F= mω2R, where m is the mass of the object, ω is the angular velocity and R is the radius of the circular path.

1) An object with more mass would be requiring less angular velocity and a smaller radius of circular motion, to maintain its circular motion.

2) If R is high, even a lower angular speed can keep an object rotating in a circular path.

3) If R is too small, then angular velocity has to be at the higher side to compensate for the small R and generate the necessary Centripetal Force required to continue the circular motion.

Centripetal Force and Centrifugal Reaction, Newton’s 3rd Law

As per Newton’s 3rd Law, Centripetal Force must be having an equal and opposite reaction force.

Yes, it has. It’s called Centrifugal Reaction. Please note that it’s not the same as Centrifugal Force. The concept of centrifugal force is completely different and we will take that one shortly.

Coming back to Centrifugal Reaction! When we rotate a piece of stone with our finger through a tied string, then the finger also feels a force which is applied by the rotating stone. This is a Centrifugal Reaction force.

Centripetal Force and Centrifugal Reaction
Diagram-2

Now as its direction is opposite to the Centripetal force (finger feels a force which tries to drag it outwards, away from its central position) , its Centrifugal and as it’s a reaction force, so we call it as Centrifugal Reaction force. (CR in Diagram 2)

Centripetal Force Vs Centrifugal force 

Difference between centripetal force and centrifugal force

Centrifugal Force is a pseudo force, it’s not real like centripetal force

Centripetal force is a real Force because it evolves due to the mutual interaction of objects or masses.

But Centrifugal force is felt only within a Rotating Frame of Reference.

If a person shares the same frame of reference as a rotating object, then that object will apparently look like a static object to that person.
The person within a rotating frame of reference will never understand the reason for Centripetal Force being applied because for him that frame of reference is static and for something static there is no need of any force to be applied.

Rather he will feel as if some external force is being applied which is pulling the entire system away from the central position and there is another force directed towards the center which is balancing the first one.

Centripetal Force-Centrifugal force-rotational frame of reference
Diagram-3

centrifugal force – pseudo force

When passengers travel in a bus and the bus takes a sharp turn, then the passengers feel a thrust in the opposite direction. Here the bus is an example of Rotating Frame of Reference and the passengers within that frame of reference feel a pseudo force, an unreal force! (see Diagram 3)

This pseudo force is called Centrifugal Force.
Read in details: Pseudo Force

The road beside the bus is a static frame of reference.

A person standing in that static frame will never reciprocate the presence of centrifugal force for that bus, to him the movement of the passengers is just because of directional inertia.

Washing machine circular motion

Let’s see how concepts of centripetal force have been intelligently implemented in a common household machine. Yes, I am talking of Washing Machine.

Washing machine works on which force?

Concepts of centripetal force is behind washing machine functionality. As clothes are put inside the drum and drum is filled with water, circular motion sets into the drum.

centripetal force-washing machine

The circular motion of the drum transmits similar motion to the clothes as well. But as the clothes are not physically attached to the center of the drum, they don’t get any centripetal force to continue the circular motion uniformly.

As a result, they tend to move in a straight line tangent to the circular path. But they face the drum body on their way, hit it forcefully and revert back. Rotating drum again injects circular motion to the clothes and this cycle continues.

But this doesn’t happen to the water droplets in the clothes. As the clothes hit the drum body, as described above, the water droplets make their way to the outside of the drum, through the holes on the drum body. And the clothes get rid of the water by the time the washing cycle completes.

Is there any contribution of centrifugal force in the washing machine operation?

No. As said above centrifugal force is a pseudo force. It does not have any contribution to the Washing machine. The centripetal force concept is behind washing machine operation.

circular motion

I hope you enjoyed. We will discuss more in this line ! Pls see the ‘Study Suggestions‘ and the VIDEO below!

 Related Study Suggestion:

1) Critical Velocity in Circular motion in vertical plane

2) Circular Motion and its relationships with linear motion

3) Wikipedia

 an Outstanding Video for you

Centripetal Force Facts you must know if you are a PHYSICS student!
centripetal force between earth and satellite
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